few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000674

5
options: Interpret the structure of expressions.

Rewrite rational expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Work with equal groups of objects to gain foundations for multiplication.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

Use polynomial identities to solve problems.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand the connections between proportional relationships, lines, and linear equations.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Represent and solve equations and inequalities graphically.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Gain familiarity with factors and multiples.

Understand solving equations as a process of reasoning and explain the reasoning.

Generate and analyze patterns.

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

Understand properties of multiplication and the relationship between multiplication and division.

Understand and apply properties of operations and the relationship between addition and subtraction.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.
problem_activity: Problem 1
Which of the following quadratic functions will result in non-real solutions?
$${{1\over2}(x-1)^2-5=0}$$
$${{1\over2}(x-1)^2+5=0}$$
$$-{{1\over2}(x-1)^2+5=0}$$
$$-{{1\over2}(x-1)^2-5=0}$$
Explain your resoning.
Problem 2
Solve the following quadratic function. Identify the number and kind of solutions.
$${g(x)={2\over3} \left({x-{1\over9}} \right)^2 -{8\over27}}$$


correct_option_index: 16

22